Abstract
Ultra High Frequency (UHF) quotes and trades are examined in high resolution and data patterns that do not correspond to plausible market activity as in Brownlees and Gallo (Comput Stat Data Anal 51(4):2232–2245, 2006) are identified. Noise patterns other than microstructure noise are isolated and diagnostic methods are evaluated accordingly. A flexible paradigm of data handling that synthesizes statistical technique and limit order book modelling is presented, extending Barndorff-Nielsen et al. (Econom J 12(3):C1–C32, 2009), which operationalises the use of expanded filtration in empirical microstructure research. Empirical evidence from the NASDAQ 100 is presented, comprehensively demonstrating that removal of non-microstructure noise from the limit order book adds significant robustness to estimation across techniques and levels of market depth.
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Notes
This representation is similar to Garman (1976).
MSFT is the second stock in the first decile has been selected over APPL due to dataset issues. We do not expect this to influence results in anyway.
References
Ait-Sahalia, Yacine, and Yu. Jialin. 2009. High frequency market microstructure noise estimates and liquidity measures. The Annals of Applied Statistics 3 (1): 422–457.
Barndorff-Nielsen, O.E., P. Reinhard Hansen, A. Lunde, and N. Shephard. 2009. Realized kernels in practice: trades and quotes. Econometrics Journal 12 (3): C1–C32.
Baruch, Shmuel, and Lawrence R. Glosten. 2019. Tail expectation and imperfect competition in limit order book markets. Journal of Economic Theory 183: 661–697.
Brogaard, Jonathan, Terrence Hendershott, and Ryan Riordan. 2019. Price discovery without trading: Evidence from limit orders. The Journal of Finance 74 (4): 1621–1658.
Brownlees, C.T., and G.M. Gallo. 2006. Financial econometric analysis at ultra-high frequency: Data handling concerns. Computational Statistics & Data Analysis 51 (4): 2232–2245.
Garman, M. B. 1976. Market microstructure. Journal of Financial Economics 3 (3): 257–275. https://doi.org/10.1016/0304-405X(76)90006-4
Gould, Martin D., Mason A. Porter, Stacy Williams, Mark McDonald, Daniel J. Fenn, and Sam D. Howison. 2013. Limit order books. Quantitative Finance 13 (11): 1709–1742.
Hampel, Frank R. 1974. The Influence Curve and Its Role in Robust Estimation. Journal of the American Statistical Association 69 (346): 383.
Hansen, Peter R., and Asger Lunde. 2006. Realized Variance and Market Microstructure Noise. Journal of Business & Economic Statistics 24 (2): 127–161.
Hasbrouck, Joel. 2019. Price Discovery in High Resolution*. Journal of Financial Econometrics, 09. ISSN 1479-8409. https://doi.org/10.1093/jjfinec/nbz027.
Jacod, Jean, Yingying Li, and Xinghua Zheng. 2017. Statistical properties of microstructure noise. Econometrica 85 (4): 1133–1174.
Kchia, Younes, and Philip Protter. 2015. Progressive filtration expansions via a process, with applications to insider trading. International Journal of Theoretical and Applied Finance 18 (04): 1550027.
Maronna, Ricardo A., and Ruben H. Zamar. 2002. Robust Estimates of Location and Dispersion for High-Dimensional Datasets. Technometrics 44 (4): 307–317.
McLeod, A.I., and W.K. Li. 1983. Diagnostic Checking ARMA Time Series Models Using Squared-Residual Autocorrelations. Journal of Time Series Analysis 4 (4): 269–273.
Miguel, Maxi San, and Raul Toral. 2000. Stochastic Effects in Physical Systems. In Instabilities and Nonequilibrium Structures VI, vol. 5, ed. Enrique Tirapegui, Servet Martinez, Enrique Tirapegui, Javier Martínez, and Rolando Tiemann, 35–127. Netherlands, Dordrecht: Springer.
Neufcourt, Léo, and Philip Protter. 2019. Expansion of a filtration with a stochastic process: the information drift. arXiv preprint arXiv:1902.06780.
OHara, Maureen. 2015. High frequency market microstructure. Journal of Financial Economics 116 (2): 257–270.
Pani, Sudhanshu. 2021. Liquidity in high resolution in limit order markets. International Journal of Financial Markets and Derivatives 8 (1): 23–49.
Rousseeuw, Peter J., and Christophe Croux. 1993. Alternatives to the median absolute deviation. Journal of the American Statistical association 88 (424): 1273–1283.
Wilkinson, Michael. 2010. Perturbation Theory for a Stochastic Process with Ornstein-Uhlenbeck Noise. Journal of Statistical Physics 139 (2): 345–353.
Acknowledgements
The authors are grateful to all the anonymous referees for their comments on previous versions of this manuscript which contributed to improving the current manuscript. We also thank Susan Thomas, Ajay Shah, Ashok Banerjee and the participants at the IGIDR (Mumbai)-IIM Udaipur, Market Microstructure workshop, Mumbai, Feb 2020, and Hong Xiang and the participants at the World Finance Conference, Norway, Aug 2021, for their comments and suggestions.
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Chakravarty, R.R., Pani, S. A Data Paradigm to Operationalise Expanded Filtration: Realized Volatilities and Kernels from Non-Synchronous NASDAQ Quotes and Trades. J. Quant. Econ. 19, 617–652 (2021). https://doi.org/10.1007/s40953-021-00252-0
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DOI: https://doi.org/10.1007/s40953-021-00252-0